Here's how I would believe it would play out with a knight dressed in full plate with sword and shield and a samurai in lamellar armor with the typical two swords, katana and wakizashi.
The knight would try to bull rush and knock the samurai off his feet with his shield. The samurai would side step the knight's initial attack and strike with his katana. Seeing that the katana could not penetrate the full plate of the knight, the samurai would change tactics.
As the knight turned to launch his second attack, he would face a violent jujutsu (precursor and more violent form of the sports oriented jiu-jitsu seen today) move that would land the knight on his back. The samurai would then draw his wakizashi, step over the knight, slightly lift the knight's helm and issue the coup de grace.
Second scenario would be same knight on horseback, armed with a lance, and same samurai, now armed with daikyu (bow).
The knight would charge and lower his lance, readying for the strike. Samurai, calmly sitting astride his horse, would draw his daikyu, aim, release, and watch as his arrow pierced the slit in the knight's visor and ended up in the knight's right eye.
Game over either way for the knight.

Thoughts?
*edited because full text did not post*
